Nonlinear Dynamic Fault Detection Method Based on Isometric Mapping

Abstract

Abstract: The data collected from chemical process are strongly nonlinear and dynamic related. To solve this problem, a nonlinear dynamic fault detection method using dynamic isometric mapping (DISOMAP) manifold learning was proposed. It first extracts submanifold feature from original data set with adaptive neighbor parameters, which preserves geometric structure. Then linear regression projection mapping which maps the original high dimension space to a low dimension embedding space is used. Finally, T2 and SPE statistics are constructed in the process monitoring application. The simulation results of Tennessee Eastman process show that DISOMAP-based method is more effective than KPCA (kernel principal component analysis) for process monitoring and fault detection.

Key words: dynamic isometric mapping (DISOMAP), manifold learning, non-linear, fault detection

CLC Number:

TP277

ZHANG Ni, TIAN Xue-Min. Nonlinear Dynamic Fault Detection Method Based on Isometric Mapping[J]. Journal of Shanghai Jiaotong University, 2011, 45(08): 1202-1206.

References

［1］Russell L H, Braatz R D. Fault detection and diagnosis in industrial system［M］. London: Springer Verlag Press, 2001.

［2］Lee J M, Yoo C K, Choi S W, et al. Nonlinear process monitoring using kernel principal component analysis［J］. Chemical Engineering Science, 2004, 59(1): 223224.

［3］Li Min，Xu Jinwu. Multiple manifolds analysis and its application to fault diagnosis［J］. Mechanical Systems and Signal Processing, 2009, 23(8): 25002509.

［4］张伟, 周维佳, 李斌. 基于分维LLE和Fisher判别的故障诊断方法［J］. 仪器仪表学报, 2010, 31(2): 325333.

ZHANG Wei, ZHOU Weijia, LI Bin. Fault diagnosis approach based on fractal dimension LLE and Fisher discriminant［J］. Chinese Journal of Scientific Instrument, 2010, 31(2): 325333.

［5］Shao Jidong, Rong Gang. Nonlinear process monitoring based on maximum variance unfolding projections［J］. Expert Systems with Applications, 2009, 36(8): 1133211340.

［6］魏宪, 李元祥, 赵海涛, 等. 基于改进ISOMAP算法的图像分类［J］. 上海交通大学学报, 2010, 44(7): 911915.

WEI Xian, LI Yuanxiang, ZHAO Haitao, et al. Image classification using modified ISOMAP method［J］. Journal of Shanghai Jiaotong University, 2010, 44(7): 911915.

［7］Elizaveta Levina, Ann Arbor Mi. Maximum likelihood estimation of intrinsic dimension［J］. Advances in Neural Information Processing Systems, 2004, 17: 777784.

［8］Tenenbaum J B, Vin de Silva, Landford J C. A global geometric framework of nonlinear dimensionality reduction［J］. Science, 2000, 290(5500): 23192323.

［9］Shao Chao, Huang Houkuan, Zhao Lianwei. A more topologically stable ISOMAP algorithm［J］. Journal of Software, 2007, 18(4): 869877.

［10］Downs J J, Vogel E F. A plantwide industrial process control problem［J］. Computers and Chemical Engineering, 1993, 17(3): 245255.

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